Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Viability of Pseudomonas aeruginosa in cough aerosols generated by persons with cystic fibrosis

Background Person-to-person transmission of respiratory pathogens, including Pseudomonas aeruginosa, is a challenge facing many cystic fibrosis (CF) centres. Viable P aeruginosa are contained in aerosols produced during coughing, raising the possibility of airborne transmission. Methods Using purpose-built equipment, we measured viable P aeruginosa in cough aerosols at 1, 2 and 4 m from the subject (distance) and after allowing aerosols to age for 5, 15 and 45 min in a slowly rotating drum to minimise gravitational settling and inertial impaction (duration). Aerosol particles were captured and sized employing an Anderson Impactor and cultured using conventional microbiology. Sputum was also cultured and lung function and respiratory muscle strength measured. Results Nineteen patients with CF, mean age 25.8 (SD 9.2) years, chronically infected with P aeruginosa, and 10 healthy controls, 26.5 (8.7) years, participated. Viable P aeruginosa were detected in cough aerosols from all patients with CF, but not from controls; travelling 4 m in 17/18 (94%) and persisting for 45 min in 14/18 (78%) of the CF group. Marked inter-subject heterogeneity of P aeruginosa aerosol colony counts was seen and correlated strongly (r=0.73–0.90) with sputum bacterial loads. Modelling decay of viable P aeruginosa in a clinic room suggested that at the recommended ventilation rate of two air changes per hour almost 50 min were required for 90% to be removed after an infected patient left the room. Conclusions Viable P aeruginosa in cough aerosols travel further and last longer than recognised previously, providing additional evidence of airborne transmission between patients with CF.

Field-effect transistors based on self-organized molecular nanostripes

Charge transport properties in organic semiconductors depend strongly on molecular order. Here we demonstrate field-effect transistors where drain current flows through a precisely defined array of nanostripes made of crystalline and highly ordered molecules. The molecular stripes are fabricated across the channel of the transistor by a stamp-assisted deposition of the molecular semiconductors from a solution. As the solvent evaporates, the capillary forces drive the solution to form menisci under the stamp protrusions. The solute precipitates only in the regions where the solution is confined by the menisci once the critical concentration is reached and self-organizes into molecularly ordered stripes 100-200 nm wide and a few monolayers high. The charge mobility measured along the stripes is 2 orders of magnitude larger than the values measured for spin-coated thin films.

Photophysical characterization of light-emitting poly(indenofluorene)s

Time-resolved photoluminescence spectroscopy experiments of three poly(2,8-indenofluorene) derivatives bearing different pendant groups are presented. A comparison of the photophysical properties of dilute solutions and thin films provides information on the chemical purity of the materials. The photophysical properties of poly(2,8-indenofluorene)s are correlated with the morphological characteristics of their corresponding films. Wide-angle X-ray scattering experiments reveal the order in these materials at the molecular level. The spectroscopic results confirm the positive impact of a new synthetic approach on the spectral purity of the poly(indenofluorene)s. It is concluded that complete side-chain substitution of the bridgehead carbon atoms C-6 and C-12 in the indenofluorene unit, prior to indenofluorene ring formation, reduces the probability of keto formation. Due to the intrinsic chemical purity of the arylated derivative, identification of a long-delayed spectral feature, other than the known keto band, is possible in the case of thin films. Controlled doping experiments on the arylated derivative with trace amounts of an indenofluorene-monoketone provide quantitative information on the rates of two major photophysical processes, namely, singlet photoluminescence emission and singlet photoluminescence quenching. These results allow the determination of the minimum keto concentration that can affect the intrinsic photophysical properties of this polymer. The data suggest that photoluminescence quenching operates in the doped films according to the Stern-Volmer formalism.

A high mobility P-type DPP-thieno[3,2-b]thiophene copolymer for organic thin-film transistors

A copolymer comprising 1,4-diketopyrrolo[3,4-c]pyrrole (DPP) and thieno[3,2-b]thiophene moieties, PDBT-co-TT, shows high hole mobility of up to 0.94 cm2 V-1 s-1 in organic thin-film transistors. The strong intermolecular interactions originated from π-π stacking and donor-acceptor interaction lead to the formation of interconnected polymer networks having an ordered lamellar structure, which have established highly efficient pathways for charge carrier transport.

Annealing-free high-mobility diketopyrrolopyrrole-quaterthiophene copolymer for solution-processed organic thin film transistors

A donor-acceptor polymer semiconductor, PDQT, comprising diketopyrrolopyrrole (DPP) and β-unsubstituted quaterthiophene (QT) for organic thin film transistors (OTFTs) is reported. This polymer forms ordered layer-by-layer lamellar packing with an edge-on orientation in thin films even without thermal annealing. The strong intermolecular interactions arising from the fused aromatic DPP moiety and the DPP-QT donor-acceptor interaction facilitate the spontaneous self-assembly of the polymer chains into close proximity and form a large π-π overlap, which are favorable for intermolecular charge hopping. The well-interconnected crystalline grains form efficient intergranular charge transport pathways. The desirable chemical, electronic, and morphological structures of PDQT bring about high hole mobility of up to 0.97 cm2/(V·s) in OTFTs with polymer thin films annealed at a mild temperature of 100 °C and similarly high mobility of 0.89 cm2/(V·s) for polymer thin films even without thermal annealing.

Electron-accepting conjugated materials based on 2-Vinyl-4,5- dicyanoimidazoles for application in organic electronics

We report the Heck coupling of 2-vinyl-4,5-dicyanoimidazole (vinazene) with selected di- and trihalo aromatics in an effort to prepare linear and branched electron-accepting conjugated materials for application in organic electronics. By selecting the suitable halo-aromatic moiety, it is possible to tune the HOMO - LUMO energy levels, absorption, and emission properties for a specific application. In this regard, materials with strong photoluminescence from blue → green → red are reported that may have potential application in organic light-emitting diodes (OLEDs). Furthermore, derivatives with strong absorption in the visible spectrum, coupled with favorable HOMO-LUMO levels, have been used to prepare promising organic photovoltaic devices (OPVs) when combined with commercially available semiconducting donor polymers.

Synthesis, characterization and organic field effect transistor performance of a diketopyrrolopyrrole-fluorenone copolymer

A diketopyrrolopyrrole (DPP) with fluorenone (FN) based low band gap alternating copolymer (PDPPT-alt-FN) has been synthesized via Suzuki coupling. PDPPT-alt-FN exhibits a deep HOMO level with a lower band gap. Fabricated organic thin film transistors using PDPPT-alt-FN as a channel semiconductor show p-channel behaviour with the highest hole mobility of 0.083 cm2 V-1 s-1 measured in air.

A low-bandgap diketopyrrolopyrrole-benzothiadiazole-based copolymer for high-mobility ambipolar organic thin-film transistors

A new, solution-processable, low-bandgap, diketopyrrolopyrrole- benzothiadiazole-based, donor-acceptor polymer semiconductor (PDPP-TBT) is reported. This polymer exhibits ambipolar charge transport when used as a single component active semiconductor in OTFTs with balanced hole and electron mobilities of 0.35 cm2 V-1s-1 and 0.40 cm 2 V-1s-1, respectively. This polymer has the potential for ambipolar transistor-based complementary circuits in printed electronics.

The use of penumbrae to define and analyse non-standard fields

Aim A new method of penumbral analysis is implemented which allows an unambiguous determination of field size and penumbra size and quality for small fields and other non-standard fields. Both source occlusion and lateral electronic disequilibrium will affect the size and shape of cross-axis profile penumbrae; each is examined in detail. Method A new method of penumbral analysis is implemented where the square of the derivative of the cross-axis profile is plotted. The resultant graph displays two peaks in the place of the two penumbrae. This allows a strong visualisation of the quality of a field penumbra, as well as a mathematically consistent method of determining field size (distance between the two peak’s maxima), and penumbra (full-widthtenth-maximum of peak). Cross-axis profiles were simulated in a water phantom at a depth of 5 cm using Monte Carlo modelling, for field sizes between 5 and 30 mm. The field size and penumbra size of each field was calculated using the method above, as well as traditional definitions set out in IEC976. The effect of source occlusion and lateral electronic disequilibrium on the penumbrae was isolated by repeating the simulations removing electron transport and using an electron spot size of 0 mm, respectively. Results All field sizes calculated using the traditional and proposed methods agreed within 0.2 mm. The penumbra size measured using the proposed method was systematically 1.8 mm larger than the traditional method at all field sizes. The size of the source had a larger effect on the size of the penumbra than did lateral electronic disequilibrium, particularly at very small field sizes. Conclusion Traditional methods of calculating field size and penumbra are proved to be mathematically adequate for small fields. However, the field size definition proposed in this study would be more robust amongst other nonstandard fields, such as flattening filter free. Source occlusion plays a bigger role than lateral electronic disequilibrium in small field penumbra size.

In pursuit of an architecture realism

The noble idea of studying seminal works to ‘see what we can learn’ has turned in the 1990s into ‘let’s see what we can take’ and in the last decade a more toxic derivative ‘what else can’t we take’. That is my observation as a student of architecture in the 1990s, and as a practitioner in the 2000s. In 2010, the sense that something is ending is clear. The next generation is rising and their gaze has shifted. The idea of classification (as a means of separation) was previously rejected by a generation of Postmodernists; the usefulness of difference declined. It’s there in the presence of plurality in the resulting architecture, a decision to mine history and seize in a willful manner. This is a process of looking back but never forward. It has been a mono-culture of absorption. The mono-culture rejected the pursuit of the realistic. It is a blanket suffocating all practice of architecture in this country from the mercantile to the intellectual. Independent reviews of Australia’s recent contributions to the Venice Architecture Biennales confirm the malaise. The next generation is beginning to reconsider classification as a means of unification. By acknowledging the characteristics of competing forces it is possible to bring them into a state of tension. Seeking a beautiful contrast is a means to a new end. In the political setting, this is described by Noel Pearson as the radical centre[1]. The concept transcends the political and in its most essential form is a cultural phenomenon. It resists the compromised position and suggests that we can look back while looking forward. The radical centre is the only demonstrated opportunity where it is possible to pursue a realistic architecture. A realistic architecture in Australia may be partially resolved by addressing our anxiety of permanence. Farrelly’s built desires[2] and Markham’s ritual demonstrations[3] are two ways into understanding the broader spectrum of permanence. But I think they are downstream of our core problem. Our problem, as architects, is that we are yet to come to terms with this place. Some call it landscape others call it country. Australian cities were laid out on what was mistaken for a blank canvas. On some occasions there was the consideration of the landscape when it presented insurmountable physical obstacles. The architecture since has continued to work on its piece of a constantly blank canvas. Even more ironic is the commercial awards programs that represent a claim within this framework but at best can only establish a dialogue within itself. This is a closed system unable to look forward. It is said that Melbourne is the most European city in the southern hemisphere but what is really being described there is the limitation of a senseless grid. After all, if Dutch landscape informs Dutch architecture why can’t the Australian landscape inform Australian architecture? To do that, we would have to acknowledge our moribund grasp of the meaning of the Australian landscape. Or more precisely what Indigenes call Country[4]. This is a complex notion and there are different ways into it. Country is experienced and understood through the senses and seared into memory. If one begins design at that starting point it is not unreasonable to think we can arrive at an end point that is a counter trajectory to where we have taken ourselves. A recent studio with Masters students confirmed this. Start by finding Country and it would be impossible to end up with a building looking like an Aboriginal man’s face. To date architecture in Australia has overwhelmingly ignored Country on the back of terra nullius. It can’t seem to get past the picturesque. Why is it so hard? The art world came to terms with this challenge, so too did the legal establishment, even the political scene headed into new waters. It would be easy to blame the budgets of commerce or the constraints of program or even the pressure of success. But that is too easy. Those factors are in fact the kind of limitations that opportunities grow out of. The past decade of economic plenty has, for the most part, smothered the idea that our capitals might enable civic settings or an architecture that is able to looks past lot line boundaries in a dignified manner. The denied opportunities of these settings to be prompted by the Country they occupy is criminal. The public realm is arrested in its development because we refuse to accept Country as a spatial condition. What we seem to be able to embrace is literal and symbolic gestures usually taking the form of a trumped up art installations. All talk – no action. To continue to leave the public realm to the stewardship of mercantile interests is like embracing derivative lending after the global financial crisis.Herein rests an argument for why we need a resourced Government Architect’s office operating not as an isolated lobbyist for business but as a steward of the public realm for both the past and the future. New South Wales is the leading model with Queensland close behind. That is not to say both do not have flaws but current calls for their cessation on the grounds of design parity poorly mask commercial self interest. In Queensland, lobbyists are heavily regulated now with an aim to ensure integrity and accountability. In essence, what I am speaking of will not be found in Reconciliation Action Plans that double as business plans, or the mining of Aboriginal culture for the next marketing gimmick, or even discussions around how to make buildings more ‘Aboriginal’. It will come from the next generation who reject the noxious mono-culture of absorption and embrace a counter trajectory to pursue an architecture of realism.